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Journals / Turkish Journal of Science / 2022 / Cilt: 7 Sayı: 3

New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions

Jamshed Nasir(COMSATS University of Islamabad)0000-0002-7141-4089
Professor Dr.(COMSATS University of Islamabad)0000-0001-7192-8269
Mustafa Ali Dokuyucu(AGRI IBRAHIM CECEN UNIVERSITY)0000-0001-9331-8592
Ahmet Ocak Akdemir(AGRI IBRAHIM CECEN UNIVERSITY)0000-0003-2466-0508
Pages
185–201
Publication Date
2022-12-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

These results can be extended to different kinds of convex functions as well as pre-invex functions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The main motivation of this study is to present new Hermite-Hadamard (HH) type inequalities via a certain fractional operators.
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Key Findings & Data:We establish two new identities and give new estimations of HH- type inequalities for differentiable and convex mapping via Katugampola-fractional operators.
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Conclusion & Impact:These results can be extended to different kinds of convex functions as well as pre-invex functions.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Convex functions · Hermite-Hadamard inequalities · Katugampola-fractional integrals

Abstract

The main motivation of this study is to present new Hermite-Hadamard (HH) type inequalities via a certain fractional operators. We establish two new identities and give new estimations of HH- type inequalities for differentiable and convex mapping via Katugampola-fractional operators. Here, we gave new Lemmas having identities for differentiable functions and construct related inequalities. Main findings of this study would provide elegant connections and general variants of well known results established recently. These results can be extended to different kinds of convex functions as well as pre-invex functions.

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Cite This Article

Nasir, J., Dr., P., Dokuyucu, M. A., Akdemir, A. O. (2022). New Variants of Hermite-Hadamard Type Inequalities via Generalized Fractional Operator for Differentiable Functions. Turkish Journal of Science, Cilt: 7 Sayı: 3, 185–201. https://ajindex.com/articles/1557505

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References (6)

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  4. A. Kilbas, H.M. Srivastava and J.J. Trujillo,Theory and applications of fractional differential equations, Elsevier B.V., Amsterdam, Netherlands, (2006).
  5. K. S. Miller and B. Ross, An introduction to fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley and Sons, Inc., New York, (1993).
  6. H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamar-Fejer type inequalityies for generalized fractional integrals, J.Math. Anal. Appl., 26(2013), 742-753.